Bras are designed to provide support for your girls. There are all kinds of little innovations that are intended to provide that support while giving you the comfort you need to get through the day. All that being said, there is no doubt that wearing bras in warmer temperatures can lead to serious sweat issues. While sweat is just a part of life, there are some steps that can be taken to deal with it.
The body is an amazing heat dispersal mechanism. The skin is the primary organ used to shed heat from our inner cores. This is done by bringing blood to just under the skin surface, opening the pours and letting heat escape. If your bra restricts the exposure of the skin to the air, this system is going to be interrupted. The cups are obviously going to do so, but that can't be avoided. If you are wearing bras that push the breasts together, however, it can. As a result, you might want to change the style of bra you wear.
A second factor to consider is the material the bra is made out of. Some materials will "breathe", which let's air get to the skin. Other materials will actually "wick" the sweat away from the skin as is found with certain sports clothing. Cotton and silk materials breathe well, but you should look into many of the new microfiber materials used with bras. The microfiber materials are tailored to different purposes and some of these are definitely sweat oriented.
At the end of the day, sweat is a natural part of the bodily process. It keeps you from overheating, which is very difficult on the body and can even lead to death in worse case scenarios. A quality bra can minimize the sweat level you experience, but no bra is ever going to completely deal with the problem. With this in mind, don't expect perfection.